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本文提出了一种基于双剪统一强度理论的统一平面应变滑移线场理论.本理论充分考虑了各种不同材料的中间主应力效应,是一种完全意义上的统一理论.各种基于其他强度理论,如Tresea,Mises和Mohr-Coulomb等的平面应变正交或非正交滑移线场理论均是本理论的特例,并且可以通过不同的加权参数b而构成一系列新的理论.本文讨论了基于刚塑性的Prandtl-Reuss假设的平面应变滑移线场理论的应用范围,证明了该假设可以由Mises屈服条件和相关联流动法则推导得出.本文还通过引入中间主应力系数m,首次提出了另外一条比刚塑性Prandtl-Reuss假设更宽的假设来反映体积可以(或不可以)压缩的材料的中间主应力,该中间主应力即是z方向的主应力.我们通过试验和弹塑性有限单元方法验证了本统一理论的正确性.本理论可以很容易地应用到众多工业领域如金属塑性成型、地基承载力预测、边坡稳定性预测等.由于双剪统一强度理论的通用性和优越性已被逐渐认识,因此,平面应变统一滑移线场理论可以应用于各种工程材料,尤其对在土木工程中广泛应用的、具有强烈中间主应力依赖性的岩土类材料,本理论会更显示出其优越性.
This paper proposes a unified planar strain-slip line field theory based on double shear unified strength theory. This theory fully considers the intermediate principal stress effects of various materials, and is a unified theory in a complete sense. Various based on other Intensity theory, such as Tresea, Mises and Mohr-Coulomb et al.’s plane strain orthogonal or non-orthogonal slip line field theory are all special cases of this theory, and a series of new theories can be formed by different weighting parameters b. The application of the planar strain-slip liner field theory based on the rigid plasticity Prandtl-Reuss hypothesis is discussed. It is proved that the hypothesis can be derived from the Mises yield condition and the associated flow rule. This paper also introduces the intermediate principal stress coefficient m. For the first time, another broader assumption is made than the rigid plasticity Prandtl-Reuss hypothesis to reflect the intermediate principal stress of a material that may (or may not) be compressed. This intermediate principal stress is the principal stress in the z direction. We pass the test and bomb. The plastic finite element method verifies the correctness of this unified theory. This theory can be easily applied to many industrial fields such as metal plastic forming and foundation bearing capacity. Measurement, slope stability prediction, etc. Since the universality and superiority of the double shear unified strength theory have been gradually recognized, the plane strain uniform slip line field theory can be applied to various engineering materials, especially in civil engineering. The widely used geotechnical materials with a strong intermediate principal stress dependence will show its superiority.